How would I go about proving the following identity:
$$\frac{1}{\left|z\right|} = \left|\frac{1}{z}\right|$$
I keep finding myself going in circles. I've tried using this identity: $|z|^2 = z^*z$ conjugate.
2026-04-22 15:22:54.1776871374
Quick complex number proof question:
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Hint: Remember that for complex numbers $a$ and $b$, $|a\cdot b| = |a|\cdot|b|$. Based on this, what can we say about $\left|z\cdot \frac{1}{z} \right|$?